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Dirk H. Rischke

Publications and source records attributed to Dirk H. Rischke.

At least 145 records · Page 8Linked to original sources
arXiv2005

Phase-Space Description of Momentum Spectra in Relativistic Heavy-Ion Collisions

We consider a phase-space model for particle production in nuclear collisions. Once the multiplicities of the individual particle species are known, single-inclusive momentum spectra can be computed after making simplifying assumptions for the matrix element for multiparticle production. Comparison of the calculated spectra with data for pions and kaons from central Pb+Pb collisions at E_{Lab}=158 AGeV reveals a residual longitudinal phase-space dominance in the final state of the reaction. We account for this by modifying the isotropic, relativistic invariant phase space in a way which retains boost invariance in beam direction but suppresses large transverse momenta. Adjusting a single parameter, we obtain a reasonably good description of transverse momentum and rapidity spectra for both pions and kaons.

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arXiv2004

Gapless phases of color-superconducting matter

We discuss gapless color superconductivity for neutral quark matter in beta equilibrium at zero as well as at nonzero temperature. Basic properties of gapless superconductors are reviewed. The current progress and the remaining problems in the understanding of the phase diagram of strange quark matter are discussed.

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arXiv2004

Evolution of Hot, Dissipative Quark Matter in Relativistic Nuclear Collisions

Non-ideal fluid dynamics with cylindrical symmetry in transverse direction and longitudinal scaling flow is employed to simulate the space-time evolution of the quark-gluon plasma produced in heavy-ion collisions at RHIC energies. The dynamical expansion is studied as a function of initial energy density and initial time. A causal theory of dissipative fluid dynamics is used instead of the standard theories which are acausal. We compute the parton momentum spectra and HBT radii from two-particle correlation functions. We find that, in non-ideal fluid dynamics, the reduction of the longitudinal pressure due to viscous effects leads to an increase of transverse flow and a decrease of the ratio $R_{out}/R_{side}$ as compared to the ideal fluid approximation.

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arXiv2004

Gauge Field Fluctuations and First-Order Phase Transition in Color Superconductivity

We study the gauge field fluctuations in dense quark matter and determine the temperature of the induced first-order phase transition to the color-superconducting phase in weak coupling. We find that the local approximation of the coupling between the gauge potential and the order parameter, employed in the Ginzburg-Landau theory, has to be modified by restoring the full momentum dependence of the polarization function of gluons in the superconducting phase.

hep-ph↗
arXiv2004

Phase diagram of dense neutral three-flavor quark matter

We study the phase diagram of dense, locally neutral three-flavor quark matter as a function of the strange quark mass, the quark chemical potential, and the temperature, employing a general nine-parameter ansatz for the gap matrix. At zero temperature and small values of the strange quark mass, the ground state of matter corresponds to the color-flavor-locked (CFL) phase. At some critical value of the strange quark mass, this is replaced by the recently proposed gapless CFL (gCFL) phase. We also find several other phases, for instance, a metallic CFL (mCFL) phase, a so-called uSC phase where all colors of up quarks are paired, as well as the standard two-flavor color-superconducting (2SC) phase and the gapless 2SC (g2SC) phase.

hep-ph↗
arXiv2004

A General Effective Action for High-Density Quark Matter

We derive a general effective action for quark matter at nonzero temperature and/or nonzero density. For this purpose, we distinguish irrelevant from relevant quark modes, as well as hard from soft gluon modes by introducing two separate cut-offs in momentum space, one for quarks, $Λ_q$, and one for gluons, $Λ_g$. We exactly integrate out irrelevant quark modes and hard gluon modes in the functional integral representation of the QCD partition function. Depending on the specific choice for $Λ_q$ and $Λ_g$, the resulting effective action contains well-known effective actions for hot and/or dense quark matter, for instance the ``Hard Thermal Loop'' or the ``Hard Dense Loop'' action, as well as the high-density effective theory proposed by Hong and others. We then apply our effective action to review the calculation of the color-superconducting gap parameter to subleading order in weak coupling, where the strong coupling constant $g \ll 1$. In this situation, relevant quark modes are those within a layer of thickness $2 Λ_q$ around the Fermi surface. The non-perturbative nature of the gap equation invalidates naive attempts to estimate the importance of the various contributions via power counting on the level of the effective action. Nevertheless, once the gap equation has been derived within a particular many-body approximation scheme, the cut-offs $Λ_q, Λ_g$ provide the means to rigorously power count different contributions to the gap equation. We recover the previous result for the QCD gap parameter for the choice $Λ_q \alt g μ\ll Λ_g \alt μ$, where $μ$ is the quark chemical potential. We also point out how to improve this result beyond subleading order in weak coupling.

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arXiv2003

Electromagnetic Meissner effect in spin-one color superconductors

It is shown that color-superconducting quark matter, where quarks of the same flavor form Cooper pairs with spin one, exhibits an electromagnetic Meissner effect. This is in contrast to spin-zero color superconductors where Cooper pairs consist of quarks with different flavors.

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arXiv2003

Gluons, tadpoles, and color neutrality in a two-flavor color superconductor

Considering cold, dense quark matter with two massless quark flavors, we demonstrate how, in a self-consistent calculation in the framework of QCD, the condensation of Cooper pairs induces a non-vanishing background color field. This background color field has precisely the right magnitude to cancel tadpole contributions and thus ensures overall color neutrality of the two-flavor color superconductor.

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arXiv2003

Effect of color superconductivity on the mass and radius of a quark star

We compare quark stars made of color-superconducting quark matter to normal-conducting quark stars. We focus on the most simple color-superconducting system, a two-flavor color superconductor, and employ the Nambu-Jona-Lasinio (NJL) model to compute the gap parameter and the equation of state. By varying the strength of the four-fermion coupling of the NJL model, we study the mass and the radius of the quark star as a function of the value of the gap parameter. If the coupling constant exceeds a critical value, the gap parameter does not vanish even at zero density. For coupling constants below this critical value, mass and radius of a color-superconducting quark star change at most by ca. 20% compared to a star consisting of normal-conducting quark matter. For coupling constants above the critical value mass and radius may change by factors of two or more.

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arXiv2003

The Quark-Gluon Plasma in Equilibrium

Our current knowledge of the quark-gluon plasma in thermodynamical equilibrium is reviewed. The phase diagram of strongly interacting matter is discussed, with emphasis on the quark-hadron phase transition and the color-superconducting phases of quark matter. Lattice QCD results on the order of the phase transition, the thermodynamical functions, the heavy quark free energy, mesonic spectral functions, and recent results for nonzero quark chemical potential are presented. Analytic attempts to compute the thermodynamical properties of strongly interacting matter, such as perturbation theory, quasiparticle models, ``hard-thermal-loop''(HTL)-resummed perturbation theory, the Polyakov-loop model, as well as linear sigma models are discussed. Finally, color-superconducting quark matter is considered in the limit of weak coupling. The gap equation and the excitation spectrum are derived. The solution of the gap equation, gap parameters in various color-superconducting phases, and critical temperatures for the transition to normal-conducting quark matter are presented. A summary of gluon and photon properties in color superconductors is given.

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arXiv2003

Chiral symmetry restoration in linear sigma models with different numbers of quark flavors

Chiral symmetry restoration at nonzero temperature is studied in the framework of the O(4) linear sigma model and the U(N_f)_r x U(N_f)_l linear sigma model with N_f=2,3, and 4 quark flavors. We investigate the temperature dependence of the masses of the scalar and pseudoscalar mesons, and the non-strange, strange, and charm condensates within the Hartree approximation as derived from the Cornwall-Jackiw-Tomboulis formalism. We find that the masses of the non-strange and strange mesons at nonzero temperature depend sensitively on the particular symmetry of the model and the number of light quark flavors N_f. On the other hand, due to the large charm quark mass, neither do charmed mesons significantly affect the properties of the other mesons, nor do their masses change appreciably in the temperature range around the chiral symmetry restoration temperature. In the chiral limit, the transition temperatures for chiral symmetry restoration are surprisingly close to those found in lattice QCD.

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arXiv2002

When the Transition Temperature in Color Superconductors is Not Like in BCS Theory

We study color superconductivity with $N_f=1,2,$ and 3 massless flavors of quarks. We present a general formalism to derive and solve the gap equations for condensation in the even-parity channel. This formalism shows that the leading-order contribution to the gap equation is unique for all color superconductors studied here, and that differences arise solely at the subleading order. We discuss a simple method to compute subleading contributions from the integration over gluon momenta in the gap equation. Subleading contributions enter the prefactor of the color-superconducting gap parameter. In the case of color-flavor and color-spin locking we identify further corrections to this prefactor arising from the two-gap structure of the quasiparticle excitations. Computing the transition temperature, $T_c$, where the color-superconducting condensate melts, we find that these contributions lead to deviations from the BCS behavior $T_c\simeq 0.57 ϕ_0$, where $ϕ_0$ is the magnitude of the zero-temperature gap at the Fermi surface.

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arXiv2002

Longitudinal gluons and Nambu-Goldstone bosons in a two-flavor color superconductor

In a two-flavor color superconductor, the SU(3)_c gauge symmetry is spontaneously broken by diquark condensation. The Nambu-Goldstone excitations of the diquark condensate mix with the gluons associated with the broken generators of the original gauge group. It is shown how one can decouple these modes with a particular choice of 't Hooft gauge. We then explicitly compute the spectral density for transverse and longitudinal gluons of adjoint color 8. The Nambu-Goldstone excitations give rise to a singularity in the real part of the longitudinal gluon self-energy. This leads to a vanishing gluon spectral density for energies and momenta located on the dispersion branch of the Nambu-Goldstone excitations.

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arXiv2001

How the quark self-energy affects the color-superconducting gap

We consider color superconductivity with two flavors of massless quarks which form Cooper pairs with total spin zero. We solve the gap equation for the color-superconducting gap parameter to subleading order in the QCD coupling constant $g$ at zero temperature. At this order in $g$, there is also a previously neglected contribution from the real part of the quark self-energy to the gap equation. Including this contribution leads to a reduction of the color-superconducting gap parameter $\f_0$ by a factor $b_0'=\exp \big[ -(\p ^2+4)/8 \big]\simeq 0.177$. On the other hand, the BCS relation $T_c\simeq 0.57\f_0$ between $\f_0$ and the transition temperature $T_c$ is shown to remain valid after taking into account corrections from the quark self-energy. The resulting value for $T_c$ confirms a result obtained previously with a different method.

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arXiv2001

Gluon self-energy in a two-flavor color superconductor

The energy and momentum dependence of the gluon self-energy is investigated in a color superconductor with two flavors of massless quarks. The presence of a color-superconducting quark-quark condensate modifies the gluon self-energy for energies which are of the order of the gap parameter. For gluon energies much larger than the gap, the self-energy assumes the form given by the standard hard-dense loop approximation. It is shown that this modification of the gluon self-energy does not affect the magnitude of the gap to leading and subleading order in the weak-coupling limit.

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arXiv2000

Debye screening and Meissner effect in a three-flavor color superconductor

I compute the gluon self-energy in a color superconductor with three flavors of massless quarks, where condensation of Cooper pairs breaks the color and flavor SU(3)_c x U(3)_V x U(3)_A symmetry of QCD to the diagonal subgroup SU(3)_{c+V}. At zero temperature, all eight electric gluons obtain a Debye screening mass, and all eight magnetic gluons a Meissner mass. The Debye as well as the Meissner masses are found to be equal for the different gluon colors. These masses determine the coefficients of the kinetic terms in the effective theory for the low-energy degrees of freedom. Their values agree with those obtained by Son and Stephanov.

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